Ok, there have been question about prehab, and correcting improper mobility, I'm not going to go into what to do for what as that depends on individual needs. I will however go into where you should be incorporating these for maximum benefit and where you typically should not be incorporating them.
I see many people doing all these at the end of their training sessions. There is a fundamental flaw with this. You just spent an entire training session reinforcing the bad movement you have! Why? To fix a movement pattern you need to break it first. Training with resistance in a bad pattern does nothing but continue to teach to you move poorly and create gradually increasing levels of compensation until greater dysfunction that prevents proper training or worse injury occurs. Do not fall into this habit.
Movement correction typically involves some light foam rolling or stick massage. LIGHT. If you use a stick and it is "U" shaped then you're not helping yourself. Followed by the mobility drill for your given problem or focus of prevention. I am NOT telling you to work on every movement problem, every time before every session. Prioritize what you need, it might vary by day. Asymmetric problems always trump anything else.
Corrections are just that, mobility drills and movement work. Use it as your warm up, if you're tiring yourself out to the point that your training is affected then you're doing too much. They should be challenging from a neuromuscular coordination stand point not a strength / resistance one. In some cases you might superset your training movement with the mobility drill for better feedback.
Brief note for your consumption, don't want to put too much info out at once.